Coefficients Definition and 805 Threads

1. You have a system of equations of the following form: x + iy = 0 -ix + z = 0 y - z = 0 or -2Sqr(5)x - iy = 0 ix - 2Sqr(5)y + 2iz = 0 -2iy -...

Homework Statement I was given a set of data from a Ion engine experiment. I fitted the data with an 8th order polynomial that seems pretty reasonable. What I want is the uncertainty in the coefficients. One way I read was through the design matrix. Homework Equations C_{ij}=(A^T A)^{-1}...

i solved homogenous but y"+y'+4y = 2sinh(T) is giving me trouble also have a hint sinh t = (e^t - e^-t)/2 also my "guess" was aE^t +Be^-t=Y maybe my guess was wrong?

Here is something that always bugged me, and I think I have an explanation for it now, but I am wondering if it is correct. Alright, the problem to me was that back when I was in Diff-eq, to use undetermined coefficients with polynomials, we would always group together the terms on one side, and...

Homework Statement So I'm doing a systems of DEs question with undetermined coefficients. After comparing coefficients, I have this: a+b=Ab+(1,0)T where a&b are vectors (2D) and A is the coefficient matrix: [2 -1] [3 -2] I know that 'a' is (1,1)T. I need to find b. I tried...

I've been doing quite a bit of reading on the Klein Paradox, though I have to admit a lot of the math goes over my head. So I was hoping you guys at PF could clarify a few things and help me check my conceptual understanding so far. I found this post...

Homework Statement Consider the use of cubic splines to interpolate a set of data. Suppose at some stage in the calculation we arrive at the following spline functions for two consecutive intervals \tilde{f_{0}} = x^{3} + ax^{2} + bx + c over the interval -1 \leq x \leq 1 \tilde{f_{1}} =...

Homework Statement f(x) = |cos x| if -\pi \leq x \leq\ \pi The Fourier series answer we should end up with is the following: 2/\pi - 4/\pi\sum\frac{-1^{k}}{(2k)^{2}-1}cos(2kx) where for the summation, k = 1 and goes to infinity. What I need to do is to actually go an solve for the...

Homework Statement Hi, I need to know the correct SI units for Einstein Coefficients (A and B) for stimulated emission (say laser). The equation I'm on about is Homework Equations \frac{A}{B} = \frac{8\pi h\nu^{3}}{c^{3}}The Attempt at a Solution after some scribbling I got to \frac{A}{B}...

Homework Statement I have that the general solution of a function is f(\rho,t)=\Sigmac(m)Jo(\alpha\rho\a) exp[-Dtm^2] where c(m) are constants. I need to find an expression for c(m) in terms of an integral Homework Equations Orthogonality relation given is \intdx x...

Homework Statement Let G be a finite abelian group and let #(n) signify the number of elements x in G which satisfy x^n = e. Find the torsion coefficients of G when #(2)=16, #(4)=32, #(3)=9, #(9)=81 and x^36=e for all x in G. Homework Equations The Attempt at a Solution I really...

Hi all, The relation between the magnitudes of the incident, reflected and transmitted waves are obtained using Fresnel coefficients. If a field moves from air to a more denser medium, which field should have a greater magnitude (reflected or transmitted)? I thought that it would be the...

Homework Statement A box with a mass of 22 kg is at rest on a ramp inclined at 45 degrees to the horizontal. The coefficients of friction between the box and the ramp are uS = 0.78 and uK = 0.65. a) Determine the magnitude of the largest force that can be applied upward, parallel to the...

Homework Statement f(t) = 1 0<=t<T/2 -1 T/2 <=t<=T ie. step function.frequency w_0 = 2pi/T Homework Equations The Attempt at a Solution What's the definition for the Fourier coefficients a_n and b_n again? Not the one in wikipedia.

Undetermined Coefficients to solve. y'''-6y''=3-cosx So I set everything up, get my system & I get an answer of y=c1+c2x+c3e^(6x)-6/37cosx+1/37sinx the book has y=c1+c2x+c3e^(6x)-6/37cosx+1/37sinx-1/4x^2. So I'm not sure where the book gets the last term, any ideas?

I am trying to solve a fourth order polynomial which is in the following form x^4+Ax^3+(B_1+B_2p)x^2-(C+Ap)x+D+Ep=0 Where A, B_1, B_2, C, D, E, are real parameters and p is a complex parameter. I have investigated many ways of solving this equation however there does not seem to be...

I was wondering since I'm trying to figure out an equivalent loss coefficient for a manifold that has a specific geometry. I have several area sections and would like to know if I can just add up the resulting loss coefficients from one section to the other. Any help would be greatly appreciated.

NonHomogeneous Equations and Undetermined Coefficients Find the particular solution; y''-10y'+25y=-18e^(5t) here is my work yp(x)=-Ae^(5t) yp'(x)=-5Ae^(5t) yp''(x)=-25Ae^(5t) plug into equation [-25Ae^(5t)]-10[-5Ae^(5t)]+25[-Ae^(5t)... Now; I have 0=-18e^(5t) which doesn't...

Explain why cell potentials are not multiplied by the coefficients in the balanced redox equation. (Use the relationship between delta G and cell potential to do this.) i know that cell potential is an intensive property but i don't know how to explain why you don't multiply the the cell...

Homework Statement Find the general solution of the given differential equation: y'' + 9y = (t^2)(e^3t) + 6 Homework Equations The Attempt at a Solution I want to first find a particular solution using the method of undetermined coefficients, but I'm not sure what I should...

Homework Statement I am trying to solve a system of two coupled ODEs. I am interested in an analytic solution if that is possible. I know it will be messy. \frac{\partial^2 U_1}{\partial x^2}+a_1\frac{\partial U_1}{\partial x^2}+b_1 U_1 = c_1 U_2 \frac{\partial^2 U_2}{\partial...

Homework Statement I have a probability distribution function (PDF) going fromi 0 to a on the y-axis and 0 to 30 on the x-axis. The function describing the PDF is the quadratic equation f(x) = a+bx+cx^2 I have to find a, b, and c. Homework Equations The Attempt at a Solution...

Homework Statement Split the function into partial fractions. 1/(w^4-w^3)Homework Equations 1/(w^4-w^3) The Attempt at a Solution I started by factoring the denominator to w^3(w-1) and re-writing the original function as (Aw^2+Bw+C)/w^3 + D/(w-1) and set it = 1/(w^3(w-1)) I end up with...

How do I go about solving a DE using the method of undetermined coeficients in a question like for example; y''-4y'+4y=2e^2x I tried assuming the yp to be Ae^2x but when I plugged it into the DE I ended up with 0=2e^2x ??

Hi, When using the method of undetermined coefficients to solve 2y'' + y' = cos(2x) + 4x + 1 I did it term by term. I figured out the first yp1 for the cos(2x). I'm just not sure what to "guess" as to the form of the yp2 for 4x+1 Does anyone know what to use as the guess?

I've been scouring the web in search of a Joule Thomson coefficient value for methane, but so far no luck. I have the volume, temperature, and specific heat as well... so I could also use the coefficient of thermal expansion for methane.. but I can't find that anywhere either! Does anyone...

Homework Statement My friend and I are attempting to figure out what the coefficient of friction is of a stack of paper (say, 100 sheets). Through our research, we've found that the coefficient of friction (\mu) is the maximum possible static friction force (F) divided by the normal force...

Problem Express \bold{S}^2 in the |j_1 j_2 ; m_1 m_2\rangle and |j_1 j_2; s m\rangle bases and find the unitary matrix, U, which takes the |j_1 j_2 ; m_1 m_2\rangle basis to the |j_1 j_2; s m\rangle basis, for spin 1/2 (s corresponds to the total angular momentum while m corresponds to the...

Homework Statement What is the difference between Static and Kinetic coefficients of friction? 2. The attempt at a solution I think Static coefficient of friction is one which refers to friction which is considered when the object is stationary and Kinetic coefficient of friction is one...

In a urine sample (Relman JCI 1961) urine is analyzed. We have a [Na] of 132 mmol/l, K of 62.7 mmol/l, Cl of 182 mmol/l, sulfate of 21.2 mmol/l and some other minor species. The ionic strenght is about 0.22 - now I need to compute the Na+K-Cl-2*SO4. So the ionic strength is higher than 0.1, but...

One can look into any precalculus book and find a proof of the addition formulas of sine and cosine. Though as most are aware there is a quick way to get the formulas by using Euler's Formula. But to get the formulas by eulers formula, you must equate coefficients with respect to the imaginary...

Hello, I have a nonlinear ODE with complex coefficients and need to solve it numerically. In general, I even understand what method I am going to use but how to develop the method for such kind of equations. Many packages (e.g. IMSL) or solver have routines to deal with the complex variables...

Homework Statement I have measurements of some response of a gene, and two factors: the gene, g=1...G and whether the patient/subject has a certain disease, t=1,2. the full model is y_{gtk}=\mu+\alpha_g+\beta_t +(\alpha\beta)_{gt}+\epsilon_{gtk} I know that to see if genes have...

I have measurements of some response of a gene, and two factors: the gene, g=1...G and whether the patient/subject has a certain disease, t=1,2. the full model is y_{gtk}=\mu+\alpha_g+\beta_t +(\alpha\beta)_{gt}+\epsilon_{gtk} I know that to see if genes have any connection at all...

Hi Sorry this may be an obvious one...can anyone help me with getting from the first to the second equation below? I'm particularly stuck with manipulating the terms inside the summations formulas. I can derive to here: \sum_{i=1}^{N}x_iy_i - N\bar{x}\bar{y} - \left(...

Differential Equation w/ Homogeneous Coefficients - y=ux substitution I am teaching myself, this problem is from ODEs by Tenenbaum and Pollard. This is not homework for a class. Homework Statement (x+y){dx} - (x-y){dy} = 0 Homework Equations y=ux, {dy} = u{dx} + x{du} The...

y'' - 3y' + 2y = et + t2 r = 1, 2 -> yc = c1et+c2e2t yp1 = Atet since Aet is a linear combination of our solution to yc. yp2 = At2+Bt+C y'p2 = 2At+B y''p2 = 2A via substitution we have 2A-3(2At+B)+2(At2+Bt+C) = t2 by isolating terms: 2At2 = t2 2A = 1 -> A = 1/2 -6At +...

Given y'(t) + i*k*y(t) - i*g*x(t) = 0 What "form" does x(t) take?

The JGM3 model of Earth's gravity is expressed in the form of coefficients C and S to Legendre polynomials in r, theta and phi which give the gravitational potential U = \sum\sum CV + SW Can anyone tell me the algorithm for calculating acceleration vector g(r, theta, phi) from the...

Hey people, So I have a problem where i have to find the transmitivity and reflectivity coefficients of a potential: V=-(n^2-1)E where (E is positive, constant and is the energy of the particle) Note: V IS NEGATIVE for n=1,2,...N. For each "n" the region is of fixed length "a" except...

Homework Statement f(x)=x^{2}+ax+b If v is one root of the quadratic then v^{2}-2 is the second root. Find all possible ordered pairs (a,b). Universal set is the set of real numbers. The Attempt at a Solution -a=v^{2}+v-2 0=v^{2}+v+a-2 By putting discriminant >=0 I get: 1-4(a-2)>=0...

Homework Statement This was a lab task in which we are asked: Determine the static and dynamic coefficients of friction for a block of wood of mass 82.2grams on a plank of wood. PART A: To determine the static coefficient we found the angle at which point the block just started to...

"Ehrenfest Urn" Problem Kramers-Moyal Coefficients and Planck-Fokker Equation (For some reason, i can't get latex to work, and the button that used to be in the text box to use it is gone. :-() Homework Statement In the "Ehrenfest Urn" Problem, a particle moves randomly in a grid of positions...

Hi, I'm trying to write a MATLAB Script to solve the Fourier series coefficients of a square wave via simultaneous equations in MATLAB. Any advice? I can write the expression out by hand, but cannot code it. Please advice.

Hello, I am stuck on a math problem for one of my engineering courses which seems fairly straight forward, but I have had little success with. The problem reads as follows: The following data has the form y=ax^b. Estimate the coefficients a+b. Given data: Y X 1...

Homework Statement Let V=Pn(C) (polynomials of nth degree with complex coefficients), where n >=1. Find a basis for W=V s.t. every f(x) belonging to the basis satisfies f(0)f(1)= -1. (Demonstrate that the set you find is linearly independent and spans W.) Homework Equations For...

Homework Statement Suppose that f(x) is a polynomial of degree n with real coefficients; that is, f(x)=a_n x^n+ a_(n-1) x^(n-1)+ …+a_1 x+ a_0, a_n,… ,a_0∈ R(real) Suppose that c ∈ C(complex) is a root of f(x). Prove that c conjugate is also a root of f(x) Homework Equations...

Homework Statement \frac {d^2x} {dt^2} -x = te^{-t} Find the general solution (I only need help on finding the particular solution). Homework Equations Well, I can easily find the complimentary solution via the characteristic equation, my problem lies in the particular solution...

Homework Statement The 68 kg climber in Fig. 4-52 is supported in the "chimney" by the friction forces exerted on his shoes and back. The static coefficients of friction between his shoes and the wall, and between his back and the wall, are 0.78 and 0.55, respectively. What is the minimum...

b_{n} = \frac{1}{\pi}\int^{\pi}_{-\pi}sin\theta sin n\theta d \theta let u = sin \theta, \ du = cos \theta d \theta dv = sin n \theta d \theta, \ v = -\frac{1}{n}cosn \theta = \left[-\frac{1}{n} sin \theta cos n \theta \right|^{\pi}_{-\pi} + \frac{1}{n} \int^{\pi}_{-\pi} cos...